# How to Probe Black Hole Entropy in Experiments

Bekenstein-Hawking entropy, associated with Sachdev-Ye-Kitaev (SYK) states of matter, can be directly probed in quantum matter experiments with thermopower measurements.

Sachdev-Ye-Kitaev (SYK) model is a model for (very) strongly interacting electrons, which is maximally chaotic and provides a simple holographic model of charged black holes with anti de Sitter horizons. The low energy theories of black holes and the SYK model coincide both at leading and sub-leading order. It was pointed out by Sachdev that this duality goes even further as the SYK state has a finite residual entropy per particle even at zero temperature, something which is typically absent in the quantum matter, but known in the field of quantum black holes as Bekenstein-Hawking entropy. However, measuring the Bekenstein-Hawking process is almost impossible on the astrophysical scale, so this concept of Quantum Gravity had never been confirmed experimentally.

In our recent paper submitted to PRX, we propose to probe the Bekenstein-Hawking entropy, associated with the SYK states, in direct quantum matter experiment through measuring quantum transport properties. In particular, measuring thermopower at low temperatures. In the SYK state, the thermopower across such an "SYK island" will be directly proportional to the entropy per particle which is a constant.

Sachdev-Ye-Kitaev model, introduced by Sachdev and Ye in condensed matter context 1993 [1], was "rediscovered" by Kitaev in 2015 and has been baptized as a "simple model fro Quantum Gravity" [2], [3]. An SYK state can be prepared in two dimensional van der Waals materials in strong magnetic fields. Thus it could be possible to explore analogues to Quantum Gravity in quantum matter experiments. This work is undergoing in collaboration with Kim and Yacoby labs at Department of Physics, Harvard University.

Further reading: Alexander Kruchkov, Aavishkar Patel, Philip Kim, Subir Sachdev, Thermoelectric power of Sachdev-Ye-Kitaev islands: Probing Bekenstein-Hawking entropy in quantum matter experiments, Phys. Rev. B 101, (2020) - Editors' Suggestion.

References:

[1] S. Sachdev and J. Ye, “Gapless spin-fluid ground state in a random quantum Heisenberg magnet,” Phys. Rev. Lett. 70, 3339 (1993).

[2] A. Y. Kitaev, “Talks at KITP, University of California, Santa Barbara,” Entanglement in Strongly-Correlated Quantum Matter (2015).

[3] S. Sachdev, “Bekenstein-Hawking Entropy and Strange Metals,” Phys. Rev. X 5, 041025 (2015).